1. Field of the Invention
This invention relates to an imaging optical system for correcting for a change of a focal point which is caused by a change in refractive index and a change of thermal expansion due to change of temperature. More particularly, the present invention relates to an imaging optical system such as a color scanner, etc. requiring sufficient resolution over a wide range of wavelengths and a high efficiency lens, etc. having a long focal length.
2. Description of the Prior Art
The focal length fluctuation .DELTA.f caused by change of temperature of an imaging optical system can be considered as a sum of two factors, i.e., fluctuation or change .DELTA.fn caused by the change of refractive index and fluctuation .DELTA.fL caused by thermal expansion.
The focal length fluctuations .DELTA.fn and .DELTA.fL with respect to a temperature change At from a reference temperature can be expressed as follows: ##EQU1## wherein: f: focal length of a lens
n: refractive index of a lens PA1 (dn/dt): rate of change of refractive index of a lens ##EQU2## coefficient of thermal expansion
The coefficient of thermal expansion is always positive without regard to the glass material of the lens. In the case of a positive lens, where a relation of focal length f&gt;0 is satisfied, if .DELTA.t&gt;0, .DELTA.fL always becomes positive from the equation (2) and if .DELTA.t&lt;0, .DELTA.fL always becomes negative.
Since the refractive index n&gt;1, in a case of a positive lens, if .DELTA.t&gt;0, .DELTA.fn becomes negative when it is formed of an ordinary glass material where the rate of change of the refractive index is positive, and if .DELTA.t&lt;0, .DELTA.fn becomes positive from the equation (1).
Therefore, in a case of a positive lens formed from ordinary glass material, since .DELTA.fL and .DELTA.fn vary inversly with each other, the focal length fluctuation .DELTA.f tends to be canceled by the lens itself. The same is true with respect to the negative lens.
In an imaging optical system such as a color scanner, etc. and a high efficiency lens, etc. having a long focal length, which may include a lens formed of a low dispersion glass such as, for example Fk01 (merchandise name, i.e., trademark, of Kabushiki Kaisha Ohara) in order to limit the chromatic aberration.
However, with low dispersion glass, in contrast with general type glass, the rate of change (dn/dt) of the refractive index with respect to change of temperature is a negative value.
When a low dispersion glass is used as a glass material, in a case of a positive lens, if .DELTA.t&gt;0, .DELTA.fn becomes positive, and if .DELTA.t&lt;0, .DELTA.fn becomes negative.
Therefore, in a case of a low dispersion glass, .DELTA.fL and .DELTA.fn vary in the same manner (i.e., directly with respect to each other). As a result, the focal length fluctuation .DELTA.f, which is the sum of .DELTA.fL and .DELTA.fn, due to temperature change tends to become large.
Also, in recent times, in order to obtain a light weight and low cost device, plastic lenses are utilized for various lens systems.
However, as the change of refractive index and coefficient of thermal expansion for a plastic lens as a result of a temperature change are large compared with a glass lens, deterioration in imaging efficiency (i.e., focusing) due to a change in focal length is great. Therefore, as result of this problem, a plastic lens is not used in an apparatus requiring no focusing, such as facsimile and image scanner. The focal length fluctuation of the plastic lens due to temperature change is caused by the change in the refractive index and coefficient of thermal expansion, and the influence of the coefficient of thermal expansion is about 1/4.about.1/3 that of the change of refractive index.
Japan Patent Publication No. Sho 61-34644 discloses a lens system having an object of reducing the focal point change due to the temperature change of the plastic lens. However, this lens system only takes into consideration the influence due to the change in refractive index and is insufficiently efficienct to reduce the effect of temperature change.